Pipe cutting machines cut pipe sections to length. In modem pipe cutting machines an integrated post-treatment of the cut-to-length pipe section takes place in the form of deburring and/or chamfering the pipe ends. It is necessary in a high-precision working of pipes to check the pipe ends individually after the working procedure, especially in order to control the chamfering angle, the wall thickness and the inside and outside diameter of the pipe end, the plane course and the front cut. External measuring stations for checking the cited parameters are basically known in the state of the art. In them, the cut-to-length pipe section is removed from the pipe cutting machine and introduced into the external measuring station. In order to measure the profile of the pipe end, mechanical sensors are used in the form of rolling heads in a known manner. This form of measuring is precise but also very time-consuming.